In the circuit of the figure f = 3.50 kV, C = 8.50 muF, R_1 = R_2 = R_3 = 0.980

Question

In the circuit of the figure f = 3.50 kV, C = 8.50 muF, R_1 = R_2 = R_3 = 0.980 M Ohm with C completely uncharged, switch S is suddenly closed (at t = 0). At t = 0, what are (a) current I_1, In resistor 1, (b) current I_2 in resistor 2, and (c) current in res-stor 3? At f = infinity (that is, after many time constants), what are (d)i_1. (e) i_2. and (f)i_3? What is the potential difference V_2 across resistor 2 at (g)t = 0 and (h)t = infinity? Number_____Units Number_____Units Number_____Units Number_____Units Number_____Units Number_____Units Number_____Units Number_____Units

Explanation / Answer

using kirchoff's loop rule

i1 = i2 + i3

loop rule in the left loop

E - i1*R1 - i2*R2 = 0

in the right loop

i2*R2 - i3*R3 = 0

Now given that R1 = R2 = R3 = R = 0.980*10^6 ohm

A.

solving above equation

i1 = 2*E/3R

i1 = 2*3500/(3*0.98*10^6)

i1 = 2.38*10^-3 Amp.

i1 = 2.38 mA

B.

i2 = E/3R = i1/2 = 1.19 mA

C.

i3 = i2 = 1.19 mA

D. Now,

At t = infinity the capacitor is fully charged and the current in the capacitor branch is zero.

thus

i1 = i2

By the loop rule

E - i1*R1 - i2*R2

E - 2*i*R

i = E/2R

i = i1 = 3500/(2*0.98*10^6) = 1.78*10^-3 Amp.

E.

i2 = 1.78*10^-3 Amp. = 1.78 mA

F.

i3 = 0,

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